To get the most out of Community and a prompt response to your question, please move this discussion to Products.
As for your question, you cannot embed forms in emails. I would also not rely on the number of clicks of that one link to register someone as it is not always the intended recipient doing the clicking, their recipient server may click the link to verify it. Thus, you risk that person getting a confirmation email for an event they never registered for. It would be easier for conversion tracking if you had the CTA direct to a landing page with the form. Then you can confidently rely on the number of those form fills as conscious registrations.